高频变压器设计

1、系数大小，脆度，硬度，温度稳定性，磁导系数与磁感应强度关系等进行考虑。最后是工作频率和噪声。工作频率可参见表5.4和图5-6。如铁芯用金属叠片构成，引 起机械振动噪声可能性较大;铁氧体磁芯产生这种噪声可能性小。不过,铁氧体磁芯有了磁场 时，会使材料有收缩或膨胀的现象，称为磁致伸缩(magnetostriction),随着会引起铁芯的机械共 振，磁致伸缩会改变磁场间负极性而至正极性。因此把铁芯变压器装在电源板上时，要留意是 否会产生机械噪声和电磁噪声，并设法滅小之。第三节高频变压器设计方法最常用的有两种方法，第一种是先求出磁芯窗口面积Aw与磁芯有效截面积化的乘积AP (AP=AwxAe,称磁芯面

2、积乘积)。根据AP值，査表找出所需磁性材料之编号；第二种是先求 出几何参数，査表找出磁芯编号，再进行设计。前者谓之AP法，后者称为Kg法。一、变压器设计方法面积乘积(AP)法1.AP法公式之推导(1.5.1)原边Np匝，副边Ns匝的变压器在NP匝上以电压V,开关工作时，根据法拉弟定律:V! = KffsNpBwA.式中fs开关工作频率(Hz);Bw工作磁通密度(T);&磁芯有效面积(n?);Kr波形系数，有效值与平均值之比正弦波时为4.44,方波时为4。 整理得：(1.5.2)铁芯窗口面积Aw乘上使用系数Ko为有效面积，该面积为原边绕组Np占据的窗口面积 NpAp与副边绕组Ns占据的窗口面积N

3、sAf之和，即KqAw = NpAp + NgAs仃.5.3)式中Ko窗口使用系数(Kol);Ap原边绕组每匝所占用面积；Aw芯窗口面积；As副边绕组每匝所占用面积。每匝所占用面积与流过该匝的电流值I和电流密度J有关,如下式所示：#(1.5.4)(1.5.5)整理式(1.5.2)(1.5.3)(1.5.4)(1.5.5)得ViKAw = IQfsBwAU + MB忑了V山+V2I2 w e KoKffsBwJ(1.5.6)AwA.即变压器窗口面积和铁芯截面积的乘积。Vil+V2b为原边和副边功率。上式表明 工作磁密Bw、开关工作频率fs、窗口面积使用系数他、波形系数&和电流密度J都影响到面积

4、的乘积。电流密度J宜接影响到温升，亦影响到AwAe，可表为：J = Ki(AwAe)x式中电流密度比例系数；X常数，由所用磁芯确定。式(1.5.6)又可表为(1.5.7)PtAwAe = K0KffsBwKj(Aw-Ae)x整理得:(1.5.8)式中 AP为Aw和Ae两面积的乘积(cm4);PT为VJi + V2I2变压器的视在功率(W);Bw工作磁通密度(T);fs开关工作频率(Hz);式(1.5.8)说明，铁芯的选择就是选择一合适的AP值,使它输送功率Pt时,铜损和铁损引 起的温升在额定温升之内。图5-8所示的常用几种铁芯AP值示意图。2.变压器视在功率Pt的确定视在功率随线路结构不同而不

5、同。如图5-9所示。163#-HErL/1DoAwT/EI左片铁芯耀形铁芯环形铁芯图5-9视在功率与线路结构关系线路(a)理想时(即变压器效率“ 1时)。 Pt二R + Po = 2R实际(即 q 1) PT=PO + = Po(l + )线路(b)理想时(n/2）线路（）理想时（耳二丨）：PT = 72Pi实际（T| Pf403590-0.1232.558.813.1金属叠片铁芯Pcu = Pfe366534-0.1241.368.219.7c型铁芯Peu = Pfe323468-0.1439.266.617.9单线圈PcuPf 395569-0.1444.576.625.6带绕铁芯Pcu

6、= Pfe250365-0.1350.982.325表5.8中各值是由各种铁芯资料使用最小平方误差法以尽就符合其函数曲线值而求得。 有关电流密度J、铁芯体积Voi、重量W,、和面积As与AP的关系表为：J=KjAFWt = KWAP75Voi = KVAI*75As = KsAF二、AP法举例一推挽方式工作的开关电源，原边接VS = 28(V),副边带中心抽头全波整流线路,输岀电 压Vo = 18(V),Io = 5(A)T作频率fs = 40kHz,效率7)= 0.98(变压器)允许温升25弋，指定用80 20谋锌铁氧体材质的C型铁芯，丄作磁通密度Bw = 0.3T,试用AP法设计高频变压器

7、各参 数。(1) 计算总的视在功率Pt设用肖特基二极管其压降Vdf = 0.6VPT =R)( + 1)V2=(Vq + Vdf)Io(+ + 1)4= (18 + 0.6x5x(g + l)V2= 265W(2) 计算AP值取 Ko = O.4Kf = 4.0(方波)Bw = 0.3Tfs = 40kHzX= -0.14由表5.8 C型铁芯允许温升25弋时査得笛=323依式(1.5.8)计算z rT x KT 、丄AP =(/265 x IO4=(3) I 01404x40x40x &x0.3x323= 0.3747(cm4)(3) 加10%裕度，由表5.9査得一型号为CL-45铁芯，其参数

8、为:AP = 0.75(cm4)MLT = 3 9cm表59 C型铁芯(部分)Ac = 0.27(cm)2Aw = 2.77 (cm)?As = 44.4(cm)2MPL = 10.4cmCAT.NO.D(CM)E(CM)F(CM)G(CM)MPL(OH)wr(CM)wm(CM)LT(CM)w”.(KG)Wj(KG)MLT(CM)arAc(CM2)GROSSAw(CM1)AP(CM1)KG(CM5)As(CM2)12345678910111213141516CL-2-E.952.476.7941.5876.12.51.72.5.019.0204.5.401.26.51 01819930.8CL

9、4.635.635.6352.2227.43.51.32.5.020.0203.9361.41.51.01842029.8CL-45.476.635.7943.49210.44.81.32.9.021.0383.9272.77.7502071044.4CL-3-D1.270.476.6351.5875.62.51.92.2.023.0185.154L01.54.02289528.4CL-5-A.952.635.6351.5876.12.91.62.5.025.0164.6.541.0154.02549828.4CL-2fiO.476.6351.1113.49210.94.81.63.5.022

10、.0604.4273.881.04.02568960.5CL-149-A.873.556.5562.6197.93.71.42.2.026.0214.1.431.46.6302621531.1CL-71.952.476柄2.5407.93.51.723.024.0324.5402.02.8102911939.0CL-7-A.952.397.6354.44511.25.21.62.1.029.0414.1342.82.95.03112644.8CL-2-C.635.794.7942.2228.13.81.43.2.028.0284.5451.76.79 Q3145539CL-76.952.476

11、.9522.5408.13.51.92.9.025.0414.8402.42.98 03311246.0CL$.952.635.6352.2227.43.51.62.5.030.0254.6541.41.76.03569833.7CL-6-E1.270.516.6352.2227.13.31.92.3.032.0265.2581.41.82.03704134.6CL62.635.6351.2702.8579.94.11.93.8.027.OM4.9.363.631.30.03780464.9CL-7.952.556.7942.5408.13.71.72.7.029.0334.7.472.02.

12、95.03828640.9CL-37.952.556.7948 43 81.72.7.030.0364.7.472.141.01.04067942.3CL-69.635.6351.2703.17510.74.41.93.8.029.0714.9.364.031.45.(M20W68.5CL-121-D.635.6351.2703.33410.94.61.93.8.030.0744.9364.231.52(M410570.4169#0.021kg#计算原边绕组的匝数仲心抽头至两端)依式(l52)$ = Vs = 28(V)P 4sBw化28 x K)44.0x40x l/x03x027 = 21

13、.5匝，取整数22匝(5) 计算原边绕组电流A= VST)(18 + 0.6)x5=28x0.98=3.39(A)(6) 计算电流密度，依式(1.5.7),由表5.8确定Kj、X,Kj = 323,X二-0.14J =Kj(AwAc)x = KjAPx =323 x (0.75)-014 =336.2A/(cm)2(7) 计算原边绕组裸线面积注意，在中间抽头电路时，Ip需乘上0.707之校正因素。IP x 0.707Axp = J3.39 x 0.707 二 336.2- = 0.00713(cm)2由导线规格表(5.10)的AWG规格査得最接近线号:AWG # 18Axp = 0.00823

14、凶= 209.5 cm表510 AWG导线规格表AWG 线 大小裸线电阻有关数据2cm2】。-，Gr-MG （注） （园密耳）戲面积直径每匝每匝cnlO3Cir-MilcmInchcmInchcm2Inch2gm/cm1052.611038432.7055.911W60.26700513.879.510.7369.200.4681141.68822641.3744.587980.2380.09384.3610.713.4889.950.37501233.08652952.0935.6470220.2130.08384.8511.916.81108.40.29771326.26518465642

15、8.3656100.1900.07495.4713.421.15136.40.23671420 82410982.8022.9545560.1710.06756.M14.826.14168.60.18791516.513260104.318.3736240.1530.06026.7716 6她.66210.60.14921613.072581131.814.7329050.1370.05397.3218.640.73262.70.11841710.392052165.811.6823230.1220.04828.1820.851.36331.20.0W3188.2281624209.59.32

16、618570.1090.04319.1323.264.33414.90.07472196.5311289263.97.53914900.09800.038610.1925.979.85515.00.0540205.1881024332.36.06511970.08790.034611.3728.998.93638.10.04726214.116812.3418.94.837954.80.07850.030912.7532.4124.0799.80.03757223.243640.1531.43.857761.70.07010.027614.2536.2155.510030.02965232.5

17、88510.8666.03.135620.00.06320.024915.8240.2191.312340.02372242.0474CM.0842.12.514497.30.05660.022317.6344.8238.615390.01884251.623320.41062.02.002396.00.05050.019919.8050.3299.719330.01498261.280252.81345.01.603316.80.04520.017822.1256.2374.224140.01185271.021201.61687.61.313259.20.04090.016124.4462

18、.1456.929470.00945280.8046158.82142.71.0515207.30.03660.014427.3269.4570.636800.00747290.6470127.72664.30.8548169.00.03300.013030.2776.9701.945270.00602300.5067100.0340220.6785134.50.02940.0116339386.2884.357030.00472310.401379.214294.60.5596110.20.02670.0105374895.2107269140.00372320.324264.005314.

19、90.455990.250.02410.009541.45105.313168488O.OO3Q5330.255450.416748.60.366272.250.02160.008546.33117.71638105650.00241340.201139.698572.80.286356250.01910.007552.48133.32095135120.00189350.158931.36108490.226844.890.01700 006758.77149.32645170600.00150360.126625.00136080.181336.000.01520.006065.62166

20、.73309213430.00119370.102620.25168010.153830.250.01400.005571.57181.83901251610.000977380.0810716.00212660.120724.010.01240.004980.35204000773390.0620712.25277750.093218.490.01090.004391.57232.66437415180.000593400.M8699.61354000.072314.440.00960.0038103.6263.28298535220.00W6441420.0397

21、27.84434050.058411.560.008630.0034115.7294.110273662600.0003790.031666.25544290.045589.000.007620.0030131.2333.313163849010.000299430.024524.84703080.036837.290.006850.0027145.8370.4162911050760.000233440.02024.00850720.031656.250.006350.0025157.4400.0189571222720.000195注图密耳是面积单位，即直径为1密耳（1密耳=0.001英寸

22、）的金属丝面积计算原边绕组电阻RP =(MLT)(N)xlO*6 cm=3.9 x 22 x 209.5 x 106= 0.018Q计算原边绕组铜损=(3.39)2 x 0.018= 0.207W（8）计算副边绕组匝数（中心抽头至两端）Vg =18 + 0.6=18.6NsNpVs22x18.6=28= 14.6匝，取整15匝（9）计算副边绕组裸线面积中间抽头变压器的Io需再乘0.707校正因素Io x 0.707Axs= j5x0.707 -336.2= 0.01051(cm)2由表510査得最接近的AWG线号为:AWG # 17Axs = 0.01039( cm)2凶= 165.8,=0.

23、165 x 103cmcm计算副边绕组电阻Rs =(MLT)(N)凶 x IO cm= 3.9x 15x 165.8x 10*6= 0.00970计算副边绕组铜耗Pscu = Io2Rs = 52X 0.0097 = 0.243W因此变压器总铜耗(原边加副边)Pcu = Ppcu + Pscu = 0.207 + 0.243 = 0.45W在绕制变压器时，应尽量选用多股线，并使多股线截面积与上面所选的AWG# 17,18截面 积相等。(10) 计算在效率T)下允许的总损耗P工P 甘-Po18.6x5_ 18,6x5=0.9 =1.9W(11) 计算允许铁耗Pfe = PE-PcU= 1.9-0

24、.45= 1.45W(12) 根据铁芯损耗曲线求工作下的实际发生的损耗 由推挽线路损耗表示式,可求出40kHz时每公斤损耗(mW)值普二 0.165 X 10-3fs(L41)Bw(L77)=0.165 x 10 x 40000 41) x 0.3(L77)= 60.53实际发生的损耗mWKg173= 60.53x0.021= 1.27W(上项损耗(1.27)小于(11)项允许(1.45)的损耗。 (14)计算单位面积损耗值Pct + Pfe0.43+1.2744.4= 0.038cm此值下温升将在25弋内，设计通过。三、变压器设计方法之二一铁芯几何参数(KJ法这是一个在AP法基础上改进的方法

25、，它从满足一定电压调整率出发的。(l) Kc公式之推导一般变压器满载与无载间输出电压有差异，其大小反映输出电压的电路内阻R,表征这 一特征用调整率GVo-V)x 100% =VV1x 100% =器X100%式中 Vo无载时电压(V)；Vj满载时电压(V)。为推导的简便，设变压器Np = Ns,各自占有窗口面积相等，因此，也有相同的电流、电压。则a =x 100 +x 100 = 200-200她x巴_妙 V V= 200 普必()另变压器原边绕组电阻R】可用下式表示：(1.5.9)D (MLT)Np(MLT)Np2AwKoi(1.5.10)式中MLT每匝平均长度;172 p电阻率，铜质l72

26、4xl(r6Q-cm;NP原边匝数；Aw窗口面积；Ko】原边绕组窗口有效使用系数(Kqi V*)。 按法拉弟定律：V! = KffeNPAcBw x 10-4(1.5.11)其中K(波形系数，等于有效值与平均值之比，正弦波时为4.44、方波时为4。由式(159)、式(15.10八式(1511)得(VA)】二蟲aCKffeNpAeBwX IO4)2200xAwNn昨小舟心x 10。2p(MLT)，铜线时p= 1.724x IO-6173(1.5.12)O,29aKf2fs2Bw2Ae2AwKoi x 104 (MLT)设原、副边窗口有效使用系数相同，为总的窗口利用系数Ko的一半即 21 = Kq

27、2 = Ko由式(1.5.12)知，算式可分为电气参数(24、兔等)和几何参数(Koi、A“、A.等)。令 Ke = 0145Kf2fs2Bw2x 10(1.5.13)(1.5.14)则变压器总伏安2(VA)i = Pt,依式(1.5.12)有PT = 2KeKGa 整理得几何参数心(1.5.15)式中心一电气参数，见式(1.5.13)a输出电压调整率，见式(1.5.9)由式(1.5.14)可知，由凡和Aw等参数决定。Ae,Aw即上节研究的AP值。因此AP与 2；的关系可推得为：AP=KPKC08式中：Kp为与铁芯型态有关的比例值，可如表5.11所示:表5.11心与铁芯型态关系表铁芯型态罐形磁

28、芯(配线芯)铁粉芯金属叠片C形铁芯Kp8.871L88.312.5四、心法举例一推挽方式工作开关电源,原边接VS = 28(V),副边为有中心抽头全波整流工作方式，输 出电压Vo= 18(V),Io = 5(A),率为40(kHz),变压器效率0.98,要求调整率v 1%,工作磁 通密度Bw = 0.3T,试设计EI型铁芯的高频变压器。(1)视在功率设整流电路二极管的压降Vdf = 0.6(V)Pt =Po(- + DV2= (18 + 0.6) x5x (命 + 1)x1.41= 265(W)(2) 计算心和耘值，依式(1.5.13),其中方波波形系数Kf = 4& =0.145Kf2fs2

29、Bw2xl0-4= 0.145x42x (40x 103)2 x 0.32 x IO4= 33408依式(1.5.15)265 -2 x 1 x 33408 =0.004(cm)5(3) 般加(2030)%裕度，设 Kg = 0.004 x (1 + 30%) =0.0052 在表 5.12 中选择最接近 的Kc值磁芯编号,并记下对应的其它参数为：型号编号 1 - 186 - 188EE Kg = 0.005783 AP = 0.24MPL = 6.4 化= 0.23 Aw= 1.06 As = 21.7 MLT = 3.8 Wtfe = 0.011哀5.12磯性材料,El与EE片行定义1.

30、D堆受厚度(CM)2. E舌片宽 (CM)3. F窗口宽(CM)4. G窗口长(CM)5. MPL磁路径长度(CM)6. HT绕制完成之变压器高= (E+G) (CM)7. WTH绕制完成之变压器宽= (E + 2F) (CM)8. LT绕制完成之变压器长= 2(E+F) (CM)9. Wlfe铁芯廈量=(祖)(人)(7.63)/1000 ()10. Wtcu铜重量=(MET)(W)(&)(8.89)/1000 (K,)11. MLT匝平均长度=2(D + 2J) + 2(E + 2J) + (3.14)(F) (CM)12. 人铁芯面积= (D)(E) (CM2)13. Aw窗口面积= (F

31、)(G) (CM2)14. AP面积乘积= (At)(W.) (CM4)15. Kc铁芯几何形状 (ApXA.XK.yMLT (CM5)16. 人表面积(CM5)El铁芯机械轮廓请看图58所示。表5.12(续)近似值近似值序号D(CM)E(CM)F(CM)G(CM)MPL(OH)HT(Ol)wni(at)ur(CM)J gWg gMLT(CM)(CM2)Aw(CM2)AP(X)&(CM5)As(aF)123456789101112131415161-3O-31EE.036.236.239.7142.41.07L0001.0012.1.06.17.010001014.12-30-31EE.472

32、.236.239.7142.41.00Q22.6.11.170200(B305.03-30-31EE.709.236.239.7142.41.01.21.0.003.0023.0.1703.0006775.91- 186-167EE.478.478.4781.7485.42.21.41.9.009.0113.6.23.63.19.00454718.52-186H.955.478M.6153.21.11.9.011OK4.R46.30.1400528613.91-186-188EE.478.478.4782.2226.42.71.41.9Oil.0143.8231.06.24.00578321.

33、72-186-188EE.955.476.4782.2226.42.71.91.9.022.0104.8.461.06.46.01650226.13-186-180EE1.433.478.4782.2226.42.72.41.9O33.0225.9.681.0673.03349930.52-312E11.590.795.9521.9847.52.83.53.5.072.056S.41.261.892.39.14425457.21-50H1.2701.270.6351.9057.63.22.53.8.094O337.71.611.211.95.16380053.22 - 26 - 27EE1.9

34、05.952.6351.7486.72.73.23.2.092.0338.31.811.112.01.17565749.61-21EI1.2701.270.7952.0658.33.32.94.1.102.O8.21.611.642.65 20865262.12-27-36EE1.905.952.6352.1137.43.13.23.2.102MO831.811.342.43.21242254.32-375EI1.9Q5.952.7951.9057.32.93.53.5.101.(M88.81.611.512.75.22607858.33-26-10EE2.857952.6351.3215.8

35、2.34.13.2.121.03010.22.72.842.28.24306354.63-112EI2.385.795.9521.9847.52.84.33.5.108.06710.01.901.893.58.27276967.23 - 26 - 27EE2.857.952.6351.7486.72.74.13.2.139.(MO10.22.721.113.02.32159260.83 - 27 - 38EE2.857.952.6352.1137.43.14.13.2.154(M910.22.72t.343.65.38890266.23-375D2.857.952.7951.9057.32.9

36、4.43.5.152.05810.72.721.514.12.41834570.42-5OH2.5401.270.6351.9057.63.23.83.8.188.04410.23.231.213.90.49243671.01-75EI1.9051.905.9522.85711.44.83.85.7.316.10911.23.632.729.881.277636119.62-75H3.8101.905.9522.S5711.44.85.75.7.633.14715.27.262.7219.753.764375159.73-75EI5.7151.905.9522.85711.44.87.65.7

37、.949.18419.010.892.7229.636.775479199.6(4) 计算Np依式(1.5.11),其中 V)= VS = 28VjxlO4KfBwfsAg_28 x IP4= 4x0.3x40x 叽0.23=26匝(5) 求原边电流Ip18.6x5=28x0.98 =3.39(A)(6) 求电流密度，依式(1.5.6)有_ P | x 104J = KoKfBwAP265 x IP4 4 x0.4 x40x 103 x 0.3 x0.24= 575A/(cm)2计算原边绕组裸线面积177Ip x 0.707Axp = j3.39x0.707575= 0.0042( cm)2由

38、表(5.10)线规表査到最接近裸线面积的导线编号为：AWG#20Axp = O.OO5188(cm)2凶= 332.3cm计算原边绕组电阻Rp =(MLT)(NP)xlO-6cm=3.8 x26x332.3x 10-6= 0.03280计算原边绕组铜损为：Ppcu = IpRp= 3.392x 0.0328= 0.3 力 W(7) 求副边绕组匝数,Vp = V1 = Vs，副边电压为Vs = 18.6% =野(1 +孟),26x_,18.6 (丄)28 u+ 1007= 17.2 匝取整17匝。计算副边绕组裸线面积。, Io X 0.707Axs= j5x0.707=0.0062( cm)2査

39、表（50）得最接近裸线面积为AWG # 190Axs = 0.006531s=263-9计算副边绕组电阻值Rs =(MLT)(Ns)xlO-6 cm= 3.8x 17 x 263.9x 1=0.017(0)计算相应铜损:Pscu = XRs= 52x 0.017 =0.425( W)在绕制变压器时，尽量选用多股线，并使多股线截面积与上面所选的AWG# 19、20截面积 相等。（9）求调整率a调整率是导线内阻的反映，也是铜耗的反映,故有：Pcu x 100百Ppgj + PscuPoxlOO0.377 + 0.42518.6x5x 100= 0.86%合乎调整率a1/丹,即气隙很小。式(1.5.31)可简表为：(1.5.32)L=吟也x108(H)&如气隙效应不能忽略，则要考虑窗口长G与气隙b比值，即磁通边缘效应因素F,可表为:(1.5.33)因此，式(1.5.32)修正为:(1.5.34)L=xlO-(H)图5-10磁感应强度与U+AI关系